The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
The complete planar S-matrix of $ \mathcal{N} = 4 $ SYM as a Wilson loop in twistor space
复制标题
DOI：
10.1007/jhep12(2010)018
复制
发表时间：
2010-09
影响因子：
5.4
通讯作者：
L. Mason;David Skinner
中科院分区：
文献类型：
--
作者：
L. Mason;David Skinner
我们证明了超杨-Mills的完整平面S矩阵--包括所有回路的所有N-k个MHV部分振幅--等价于扭曲空间中超对称威尔逊回路的关联函数。值得注意的是，整个经典S矩阵都是由计算自对偶扇区的关联函数产生的，而关联函数按杨-米尔斯耦合常数的幂展开则提供了振幅的环路展开。我们通过对n个粒子的NMHV和N2个MHV树、1圈MHV和NMHV振幅的被积以及n个粒子的2圈MHV振幅的显式计算来支持我们的建议。这些计算是利用轴向压力计中的扭矩作用进行的。在这个规范中，关联函数的费曼图是通常的散射幅度的MHV图的平面对偶。结果以(动量)扭曲空间中对偶超共形不变量的乘积和的形式给出，并与文[1]中直接从MHV规则导出的表达式一致。扭转空间的威尔逊环是用于计算MHV振幅的标准威尔逊环的自然超对称推广。我们展示了彭罗斯-沃德变换如何在时空上确定相应的超对称化，并在阿贝尔情形下给出了相应的超连接。
We show that the complete planar S-matrix ofsuper Yang-Mills—including all N k MHV partial amplitudes to all loops—is equivalent to the correlation function of a supersymmetric Wilson loop in twistor space. Remarkably, the entire classical S-matrix arises from evaluating the correlation function in the self-dual sector, while the expansion of the correlation function in powers of the Yang-Mills coupling constant provides the loop expansion of the amplitudes. We support our proposal with explicit computations of the n particle NMHV and N 2 MHV trees, the integrands of the 1-loop MHV and NMHV amplitudes, and the n particle 2-loop MHV amplitude. These calculations are performed using the twistor action in axial gauge. In this gauge, the Feynman diagrams of the correlation function are the planar duals of the usual MHV diagrams for the scattering amplitude. The results are presented in the form of a sum of products of dual superconformal invariants in (momentum) twistor space, and agree with the expressions derived in the companion paper [1] directly from the MHV rules. The twistor space Wilson loop is a natural supersymmetric generalization of the standard Wilson loop used to compute MHV amplitudes. We show how the Penrose-Ward transform can be used to determine a corresponding supersymmetrization on space-time and give the corresponding superconnection in the abelian case.